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<p>In this paper, we optimize the response of elasto-plastic truss structures by tailoring their nonlinear force–displacement behavior to match a prescribed target curve. The resulting inverse design problem is addressed indirectly through a sequence of surrogate sub-problems, each based on a first-order approximation of the nonlinear response. At every iteration, the solution of the current sub-problem is used to update both the design and the response approximation, enabling an iterative progress toward the final design. The force–displacement response is evaluated using a displacement-controlled numerical scheme. We present two formulations for approximating the response: one based on equivalent static displacements and another based on a direct Taylor expansion. Both rely on first-order information computed at intermediate design points. The proposed methodologies are benchmarked against the conventional approach, which solves the reference problem by directly considering its nonlinear response. Our results indicate that the proposed approaches require fewer nonlinear response evaluations to achieve an optimal design. We also observe a stable evolution of design updates due to the use of a trust region. In some cases, our approaches converge to final designs characterized by optimized objective values comparable to those obtained by directly solving the reference problem, but with different structural layouts. This is likely motivated by the presence of multiple local minima with similar performance within the non-convex design space. The code to reproduce one of the examples is available at: <Emphasis FontCategory="NonProportional">https://github.com/hjalgra/ep-truss-ipopt</Emphasis>.</p>

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Optimization of elasto-plastic trusses through sequential linear response approximation

  • 期刊论文

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  • 发表日期：

    2026年7月3日

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  • Hendrik J. Algra,
  • Nicolò Pollini

摘要

In this paper, we optimize the response of elasto-plastic truss structures by tailoring their nonlinear force–displacement behavior to match a prescribed target curve. The resulting inverse design problem is addressed indirectly through a sequence of surrogate sub-problems, each based on a first-order approximation of the nonlinear response. At every iteration, the solution of the current sub-problem is used to update both the design and the response approximation, enabling an iterative progress toward the final design. The force–displacement response is evaluated using a displacement-controlled numerical scheme. We present two formulations for approximating the response: one based on equivalent static displacements and another based on a direct Taylor expansion. Both rely on first-order information computed at intermediate design points. The proposed methodologies are benchmarked against the conventional approach, which solves the reference problem by directly considering its nonlinear response. Our results indicate that the proposed approaches require fewer nonlinear response evaluations to achieve an optimal design. We also observe a stable evolution of design updates due to the use of a trust region. In some cases, our approaches converge to final designs characterized by optimized objective values comparable to those obtained by directly solving the reference problem, but with different structural layouts. This is likely motivated by the presence of multiple local minima with similar performance within the non-convex design space. The code to reproduce one of the examples is available at: https://github.com/hjalgra/ep-truss-ipopt.